Bundle: Physical Chemistry, 2nd + Student Solutions Manual
Bundle: Physical Chemistry, 2nd + Student Solutions Manual
2nd Edition
ISBN: 9781285257594
Author: David W. Ball
Publisher: Cengage Learning
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 16, Problem 16.15E
Interpretation Introduction

Interpretation:

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are to be calculated.

Concept Introduction:

The change in energy (ΔE) of the state depends on the strength of the magnetic field (B) and the z-component quantum number (ML) in the presence of magnetic field. The expression for the change in energy (ΔE) is written below.

ΔE=μBMLB

The value of (ML) can be positive, negative or zero. Hence, the change in energy (ΔE) can be positive, negative or zero. The change in energy (ΔE) of the state is equal to the amount of splitting.

Expert Solution & Answer
Check Mark

Answer to Problem 16.15E

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are 3.10×1024J, 1.03×1024J, +1.03×1024J and +3.10×1024J.

Explanation of Solution

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are calculated by the formula given below.

ΔE=gμBMJB…(1)

Where,

μB is Bohr magneto (9.274×1024J/T).

(MJ) is the z-component quantum number.

g is Lande g factor.

B is earth’s magnetic field.

The value of g is calculated by the formula given below.

g=1+j(j+1)+s(s+1)l(l+1)2j(j+1)…(2)

Where,

j, s and l are quantum numbers.

The values of j, s and l for (4F3/2) state are 3/2, 3/2 and 3.

Substitute the values of j, s and l in equation (2).

g=1+3/2(3/2+1)+3/2(3/2+1)3(3+1)2×3/2(3/2+1)=1+15/4+15/41230/4=1+30/41230/4=118/430/4

Simplify the above equation.

g=135=25

One gauss equals to 1.0×104T. Therefore 5.57×103G will be equal to 0.557T.

The value of μB and B are (9.274×1024J/T) and 0.557T.

Substitute the values of μB, B and g in equation (1).

When MJ=(32),

ΔE=gμBMJB=25×9.274×1024J/T×(32)×0.557T=(35)×5.165×1024J=3.10×1024J

When MJ=(12),

ΔE=gμBMJB=25×9.274×1024J/T×(12)×0.557T=(15)×5.165×1024J=1.03×1024J

When MJ=0, ΔE will be zero.

When MJ=32,

ΔE=gμBMJB=25×9.274×1024J/T×32×0.557T=35×5.165×1024J=3.10×1024J

When MJ=12,

ΔE=gμBMJB=25×9.274×1024J/T×12×0.557T=15×5.165×1024J=1.03×1024J

Conclusion

The ΔE values experienced by the ground state (4F3/2) energy levels of V atom are 3.10×1024J, 1.03×1024J, +1.03×1024J and +3.10×1024J.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
Write the complete common (not IUPAC) name of each molecule below. Note: if a molecule is one of a pair of enantiomers, be sure you start its name with D- or L- so we know which enantiomer it is. molecule Ο C=O common name (not the IUPAC name) H ☐ H3N CH₂OH 0- C=O H NH3 CH₂SH H3N ☐ ☐ X G
(Part A) Provide structures of the FGI products and missing reagents (dashed box) 1 eq Na* H* H -H B1 B4 R1 H2 (gas) Lindlar's catalyst A1 Br2 MeOH H2 (gas) Lindlar's catalyst MeO. OMe C6H1402 B2 B3 A1 Product carbons' origins Draw a box around product C's that came from A1. Draw a dashed box around product C's that came from B1.
Classify each of the amino acids below. Note for advanced students: none of these amino acids are found in normal proteins. X CH2 H3N-CH-COOH3N-CH-COO- H3N-CH-COO CH2 CH3-C-CH3 CH2 NH3 N NH (Choose one) ▼ (Choose one) S CH2 OH (Choose one) ▼ + H3N-CH-COO¯ CH2 H3N CH COO H3N-CH-COO CH2 오오 CH CH3 CH2 + O C CH3 O= O_ (Choose one) (Choose one) ▼ (Choose one) G
Knowledge Booster
Background pattern image
Chemistry
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Chemistry & Chemical Reactivity
Chemistry
ISBN:9781337399074
Author:John C. Kotz, Paul M. Treichel, John Townsend, David Treichel
Publisher:Cengage Learning
Text book image
Chemistry: The Molecular Science
Chemistry
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781133611097
Author:Steven S. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry
Chemistry
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Cengage Learning
Text book image
Chemistry: An Atoms First Approach
Chemistry
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Cengage Learning
Text book image
Chemistry for Engineering Students
Chemistry
ISBN:9781337398909
Author:Lawrence S. Brown, Tom Holme
Publisher:Cengage Learning
The Bohr Model of the atom and Atomic Emission Spectra: Atomic Structure tutorial | Crash Chemistry; Author: Crash Chemistry Academy;https://www.youtube.com/watch?v=apuWi_Fbtys;License: Standard YouTube License, CC-BY